k = number of groups = k = 3 and N = total observations = 18
The Overall Mean = (159 + 142 + 134) / 3 = 145
DF Between = k - 1 = 3 - 1 = 2
DF error = N - k = 18 - 3 = 15
(a) SS between = SUM [n * ( - Overall Mean)2] = 6 * (159 - 145)2 + 6 * (142 - 145)2 + 6 * (134 - 145)2 = 1956
(b) MS between = SS between / DF between = 1956/2 = 978
(c) SS error = SUM [(n - 1) * Variance] = (5 * 311.6) + (5 * 91.6) + (5 * 151.6) = 2774
(d) MS error = SS error / DF error = 2774 / 15 = 184.9
(e) The ANOVA Table is as Below.
Source | SS | DF | Mean Square | F |
Between | 1956 | 2 | 978 | 5.29 |
Within/Error | 2774 | 15 | 184.9 | |
Total | 4730 | 17 |
(f) The p value for F = 2.29, DF between = 2, DF error = 15 is 0.0183
Therefore 0.01 < p value < 0.05
Conclusion: Since p value is < 0.05, Reject H0.
e. Set up the ANOVA table for this problem. Round all Sum of Squares to nearest...
The following data are from a completely randomized design. Treatment 164 149 142 157 167 124 145 149 149 137 169 136 156 142 144 141.6 119.6 126 122 133 141 152 130 134 Sample mean Sample variance a. Compute the sum of squares between treatments. Round the intermediate calculations to whole number 1488 b. Compute the mean squ are between treatments. 744 c. Compute the sum of squares due to error. 135.33 d. Compute the mean square due to...
The following data are from a completely randomized design. A 164, 142, 169, 145, 149, 167 Sample mean 156 Sample variance 144. B 147, 156,127, 147, 131, 144 Sample mean 142 Sample variance 119.2 C 124, 121, 134, 141, 158, 126, sample mean 134 sample variance 191.6. (1) Compute the sum of squares between treatments. (2) Compute the mean square between treatments. (3) Compute the sum of squares due to error. (4) Compute the mean square due to error (to...
The following data are from a completely randomized design. Treatment 163 145 123 142 157 121 166 129 132 144 145 144 148 138 153 191 138 131 159 142 134 344.8 88.8 152.8 Sample mean Sample variance a. Compute the sum of squares between treatments. Round the intermediate calculations to whole number. b. Compute the mean square between treatments. c. Compute the sum of squares due to error. d. Compute the mean square due to error (to 1 decimal).
The following data are from a completely randomized design. Treatment 145 145 145 149134 151 140 129 Sample mean Sample variance a. Compute the sum of squares between treatments. 159 310 142 108.8 134 145.2 b. Compute the mean square between treatments. c. Compute the sum of squares due to error d. Compute the mean square due to error (to 1 decimal), e. Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers....
Given a one way Anova and given the sum of squares for error is 28, the sum of squares between treatments is 86 the mean square error is 7 and the mean square between treatments is 12.5 , Compute the F statistic ?
What is the treatment sum of squares? What is the error sum of squares? What is the treatment mean square? What is the block mean square? What is the mean square error? What is the value of the F statistic for blocks? Can we reject the Null Hypothesis? Why? Test H0: there is no difference between treatment effects at α = .05. Block Treatment Mean Treatment Tr1 T2 Tr3 Block Mean 2 1 3 1 4 4 რ Nw NN...
Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between Treatments 64 8 Within Treatments (Error) 2 Total 100 The number of degrees of freedom corresponding to between-treatments is a. 3. b. 4. c. 2. d. 18.
Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom F Mean Square 180 3 Between treatments Within treatments (Error) Total 480 18 Refer to Exhibit 13-5. The mean square between treatments (MSTR) is a. 300 b. 60 O c. 15 O d. 20
Source Between treatments Within treatments Sum of Squares (Ss) df Mean Square (MS) 2 310,050.00 2,650.00 In some ANOVA summary tables you will see, the labels in the first (source) column are Treatment, Error, and Total Which of the following reasons best explains why the within-treatments sum of squares is sometimes referred to as the "error sum of squares"? O Differences among members of the sample who received the same treatment occur when the researcher O Differences among members of...
Consider the following table: SS DF MS F Among Treatments 5917.15 1183.43 4.26 Error ? Total 9253.99 17 Step 1 of 8: Calculate the sum of squares of experimental error. Please round your answer to two decimal places. Step 2 of 8: Calculate the degrees of freedom among treatments. Step 3 of 8: Calculate the degrees of freedom of experimental error. Step 4 of 8: Calculate the mean square of the experimental error. Please round your answer to two decimal...